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Re: OMEGA BLOCK with mixture model?

From: Leonid Gibiansky <LGibiansky>
Date: Thu, 16 Apr 2009 08:22:01 -0400

Another difference between BLOCK(2) and DIAG(3) is that they provide
different number of ETAs for the individual fit. I am a bit surprised
that one-compartment model with random effects on CL, V, and F is
identifiable (even with diagonal OMEGA). Indeed, for each subject, this
model has 3 free parameters. The only thing that allows to identify them
separately is the distributional assumption. It could be rather week so
I would expect higher variance values with DIAG(3) versus BLOCK(2).

How often have you used ETAs on CL, V, and F in the same one-compartment
model (without IV arm)? Is it always stable (or at least as stable as


Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
e-mail: LGibiansky at
tel: (301) 767 5566

Mats Karlsson wrote:
> Hi Steve,
> For a one-compartment model I think these are differences:
> 1) DIAG(3) is more restrictive than BLOCK(2) in the sense that only positive
> correlation between CL/F and V/F can be estimated
> 2) DIAG(3) is less restrictive than BLOCK(2) in the sense that different
> transformations can be used for F
> 3) DIAG(3) provides an EBE that can be used for diagnostic purposes (DIAG(3)
> and BLOCK(2) would give the same estimates for the same model so I don't
> understand your comment of var(F) being higher than cov(CL/F,V/F))
> 4) DIAG(3) may facilitate covariate model building (although this is minor
> as you with BLOCK(2) can put the same relationship in in two places)
> 5) If there truly is a mixture in F1, then I think DIAG(3) has a advantages
> over BLOCK(2) in number of parameters (two fewer) needed to describe the
> variability model
> 6) If some additional assumptions can be reliably made, such as all
> variability in F1 is truly in bioavailability and bioavailability is
> restricted to be between 0 and 1, some additional info may be extracted from
> the data for example by .
> I would not rank any of these as major differences (expect possibly the
> mixture aspect which I've never tried).
> For two- or three-compartment models the advantages are that if indeed the
> main covariance structure between CL/F, V1/F, Q/F, V2/F is a joint positive
> correlation due to variability in bioavailability, fu etc, then a DIAG(5) is
> more parsimonious than a BLOCK(4).
> Mats
> Mats Karlsson, PhD
> Professor of Pharmacometrics
> Dept of Pharmaceutical Biosciences
> Uppsala University
> Box 591
> 751 24 Uppsala Sweden
> phone: +46 18 4714105
> fax: +46 18 471 4003
> -----Original Message-----
> From: Stephen Duffull [mailto:stephen.duffull
> Sent: Thursday, April 16, 2009 10:13 AM
> To: Mats Karlsson; drmould
> nmusers
> Subject: RE: [NMusers] OMEGA BLOCK with mixture model?
> Mats
>> With oral data only I would normally model with BLOCK(2) on
>> CL/F and V/F or a DIAG(3) on CL/F, V/F and relative F. The
>> latter may have some advantages for diagnostics, covariate
>> model building etc.
> I have often seen these two options considered. I am unclear as to the
> advantages of DIAG(3) over BLOCK(2)? In theory it would seem that they
> should be identical. In practice it seems that DIAG(3) is more relaxed
> since it is not required that the variance of relative F if reassigned to
> the covariance of (CL/F, V/F) [under BLOCK(2)] yields a positive definite
> matrix.
> I presume an advantage wrt covariate model building would be access to the
> EBEs of F_i. However, given the variance of F_i may exceed the covariance
> of (CL/F, V/F) then I wonder if this is a real advantage or an artefact of
> numerical procedures?
> I am keen to learn more about real advantages of application of DIAG(3) as
> an alternative to BLOCK(2).
> Steve
> --
> Professor Stephen Duffull
> Chair of Clinical Pharmacy
> School of Pharmacy
> University of Otago
> PO Box 913 Dunedin
> New Zealand
> E: stephen.duffull
> P: +64 3 479 5044
> F: +64 3 479 7034
> Design software:
Received on Thu Apr 16 2009 - 08:22:01 EDT

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